course Phy121
9/20/2009 around 4:15 pm.I submitted this assignment minutes before and realized that I did not put my information on it as far as access code, email, and name. I am resubmitting. I am sorry for the inconvience.
Rotating Straw Experiment
Spin the straw and time it
The straw has a hole drilled in it, near its center point. If you trim the straw at the short flexible segment then the hole should be approximately in the middle of the remaining section of the straw. The hole should be within a millimeter or so of the center of the trimmed straw. A little extra trimming on one end or the other might be necessary to make it so.
The die has a hole drilled in or near the middle of one of its faces.
• Place the die on a level tabletop.
• Place the straw on the die, as demonstrated in one of the video clips you viewed under the line Introduction to Key Systems under the Introductory Assignment.
• Spin the straw (not too fast, so you can count its revolutions) and see how many times it goes around before stopping.
Now repeat the spin but this time use the TIMER to determine how long it takes to come to rest after being spun, and through how many revolutions it travels. You can hold onto the clip with one hand and extend a finger of that hand to start the straw spinning, leaving your other hand free to operate the TIMER.
A revolution consists of a 360-degree rotation of the straw about the axis. You should easily be able to count half-revolutions and then estimate the additional number of degrees, to come up with the rotation within an error of plus or minus 15 degrees or so. That's all the precision required here, so there is no need to bother with a protractor.
In the box below:
• Report in the first line the time in seconds and the number of degrees of rotation from the time you released the straw to the instant it came to rest. Use comma-delimited format.
• Starting in the second line give a brief description of what you did and how you made your measurements, and be sure to indicate whether you used a trimmed or untrimmed straw.
Put weights in the ends of the straw and repeat
Now insert the two bolts into the ends of the straw. If they won't work or if you don't have the bolts yet, slide a large paper clip or two onto each end. If necessary elevate the die a bit to keep the clips from dragging (for example you could set it on top of an inverted drinking glass or mug). Spin the straw. If it is unbalanced you can move one bolt (or paper clip) in or out a little, or if necessary trim whichever end needs it, a little at a time, until you achieve good balance. Then repeat the above exercise.
In the box below
• Report in the first line the time in seconds and the number of degrees of rotation from the time you released the straw to the instant it came to rest.
• Use comma-delimited format. In the second line give the length of your straw and the units in which you measured the length. Starting in the third line give a brief description of what you did and how you made your measurements.
Time at least a few 180-degree intervals and find midpoint clock times for intervals
Repeat one more time. This time click the TIMER every time an end of the straw passes a selected point, so that you will have a timing for every 180 degrees of rotation. From the data you obtain determine the average velocity of the straw, in degrees per second (this quantity is actually called 'angular velocity' because it is measured in units of angle per unit of time), for each 180 degree rotation.
Also calculate the clock time at the midpoint of each timed interval. Recall that 'clock time' is the time on a running clock.
• The second column of the TIMER represents clock times; the third column represents time intervals. Several trials are typically included in TIMER output. However in the process of analysis it is more convenient to think of a different clock for each trial.
• The running clock for a given trial (e.g., a given spin of the strap) is generally assumed to read t = 0 at the initial instant.
• The initial instant for a given trial would usually be the instant of the first 'click' of that trial.
• Clock times can be found by successively adding up the time intervals. If you have time intervals of, say, 3 s, 5 s, 9 s and 15 s, then if the clock is started at t = 0 the clock times of the corresponding events would be 3 s, 8 s, 17 s and 32 s.
• Clock times can also be found by subtracting the TIMER's clock time for the first 'click' of a trial from the clock time of each subsequent 'click'. For example the TIMER might show clock times of 63 s, 66 s, 71 s, 80 s and 95 s during a trial. This means that the second 'click' occurred 66 s - 63 s = 3 s after the initial click; the third click was 71 s - 63 s = 8 s after the initial click; the fourth and fifth clicks would have occurred 80s - 63 s = 17 s and 95 s - 63 s = 32 s after the initial 'click'. So the corresponding clock times would have been t = 0 (corresponding to TIMER clock time 63 s), then 3 s, 8 s, 17 s and 32 s.
• The midpoint clock times would be the clock times in the middle of the intervals. In the preceding example the first interval runs from clock time t = 0 to t = 3 s, so the midpoint clock time is 1.5 s. The second interval runs from t = 3 s to t = 8 s, so the midpoint clock times is the midpoint of this interval, t = 5.5 sec. The midpoints of the remaining two intervals would be t = 12.5 sec and t = 24.5 sec.
• A clock time is generally designated by t, and if t is used for the variable then it refers to clock time. A time interval is generally referred to by `dt; a time interval is a change in clock time. A midpoint clock time might be referred to as t_mid.
Copy the relevant part of the TIMER output into the box below.
Starting in the second line after your TIMER output, give a table of average velocity vs. midpoint clock time (each line should include the midpoint clock time, then the average velocity for one time interval).
Starting in the line below your table, explain how you used your data to calculate your average velocities and the midpoint clock times.
What is your evidence that the straw is speeding up or slowing down? Is there any way you can determine in a meaningful way the rate at which the straw is speeding up or slowing down?
Measure the lengths of two opposing rubber bands
Now choose one of the thin rubber bands and one of the thicker rubber bands. Make sure there are no obvious defects on the rubber band you choose; otherwise your choice should be random.
Bend three paperclips to form hooks. Hook each rubber band to an end of one hook, and attach the other hooks to the free ends of the rubber band. Pull gently on the end hooks until the rubber bands pretty much straighten out and take any data necessary to determine their lengths, as accurately as is reasonably possible with the paper rulers.
Now pull a little harder so the rubber bands stretch out a little. Stretch them so that the distance between the end hooks increases by about 1 cm. Take data sufficient to determine the lengths of the two rubber bands.
Repeat so that the distance between the end hooks increases by another centimeter, and again take data sufficient to determine the two lengths.
Repeat twice more, so that with your last set of measurements the hooks are 4 cm further apart than at the beginning.
In the box below
• Report in the first line the lengths as determined by your first measurements, with the 1 cm stretch. Report in comma-delimited form, with the length of the thicker rubber band first.
• In the second, third and fourth lines make a similar report for the three additional stretches.
• Starting in the fifth line, give a summary of how you made your measurements, your raw data (what you actually observed--what the actual readings were on the paper ruler) and how you used your raw data to determine the lengths.
Sketch a graph of length_thin vs. length_thick, where length_thin is the length of the thin rubber band and length_thick is the length of the thick rubber band.
• Fit the best straight line you can to the data, using manual fitting methods (i.e., actually draw the line on the graph--don't use a graphing calculator or a spreadsheet to find the equation of the line, but measure everything as in the Fitting a Straight Line to Data activity).
In the box below
• Give in the first line the slope and vertical intercept of your straight line.
• Starting in the second line, discuss how well the straight line actually fit the data, whether the data seems to indicate curvature, and what the slope and vertical intercept mean in terms of your rubber band system:
Observe 2 rubber bands in series vs. a single rubber band
Flip a coin.
• If it comes up Heads, add a paper clip and a second thin rubber band to the system in s such a way that your system can be viewed as a chain of two thin rubber bands pulling on a single thick rubber band.
• If it comes up Tails, instead add a second thick rubber band in such a way that your system can be viewed as a chain of two thick rubber bands pulling on a single thin rubber band.
Repeat the experiment using this system. Observe the length of the 2-rubber-band chain vs. the length of the 1-rubber-band chain. Report the slope of your graph in the box below below. Starting in the second line, discuss
• how the slope of the this graph differs from that of your previous graph
• why the slope should differ
• how you would expect the slope to differ if the two thin rubber bands were identical
• to what extent your results support the hypothesis that the two thin rubber bands do not in fact behave in identical ways.
Your instructor is trying to gauge the typical time spent by students on these experiments. Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades:
• Approximately how long did it take you to complete this experiment?
You may add optional comments and/or questions in the box below.
Your optional message or comment:
How long did it take you to complete this experiment?0
2 seconds,less than 180 degrees. I use a trimmed straw.
How long did it take you to complete this experiment?1
3 seconds, 540 degrees. 17.25cm I placed 1 paper clip on each end of the straw and tapped the end with a domino while the straw was on the die.
How long did it take you to complete this experiment?2
1 3122.535 3122.535 2 3123.25 .7148438 3 3123.977 .7265625 4 3125.25 1.273438 5 3127.809 2.558594 2,251.748degrees/s 4,247.593 degrees/s 6,141.398 degrees/s 8,70.740 degrees/s I divided 180 degrees by the time interval to get the average velocity at the midpoints.
How long did it take you to complete this experiment?3
The time intervals have more time in between them as each time interval goes on.
How long did it take you to complete this experiment?4
8.5cm,9cm 9cm,10cm 9cm,11cm 9.5cm,13cm I stretched the rubber bands and measured with a ruler. I noticed that the thinner rubber band gave more and stretche further than the ticker one did.
How long did it take you to complete this experiment?5
slope = 1.174 vertical intercept of the line I drew is 4.5. There was very little change in the stretch of the thich rubberband but the thinner gave more easily.
How long did it take you to complete this experiment?6
The slope was a little steeper because the thinner rubberbands stretched furthur than the thick one did.
How long did it take you to complete this experiment?
1 hour
Optional additional comments and/or questions:
This looks OK but I'm going to have to ask you to resubmit it once more, using the form for the experiment rather than the Submit Work Form. If you don't have your original copy, don't redo it, but let me know.